Simplify the following expression: $\dfrac{33x^2}{12x^3}$ You can assume $x \neq 0$.
Solution: $ \dfrac{33x^2}{12x^3} = \dfrac{33}{12} \cdot \dfrac{x^2}{x^3} $ To simplify $\frac{33}{12}$ , find the greatest common factor (GCD) of $33$ and $12$ $33 = 3 \cdot 11$ $12 = 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(33, 12) = 3 $ $ \dfrac{33}{12} \cdot \dfrac{x^2}{x^3} = \dfrac{3 \cdot 11}{3 \cdot 4} \cdot \dfrac{x^2}{x^3} $ $\phantom{ \dfrac{33}{12} \cdot \dfrac{2}{3}} = \dfrac{11}{4} \cdot \dfrac{x^2}{x^3} $ $ \dfrac{x^2}{x^3} = \dfrac{x \cdot x}{x \cdot x \cdot x} = \dfrac{1}{x} $ $ \dfrac{11}{4} \cdot \dfrac{1}{x} = \dfrac{11}{4x} $